If an apparatus comprises a function for transposing from baseband to the carrier frequency (and conversely, from the carrier to baseband) achieved entirely or partially in an analogue manner, it is necessary to use an IQ modulator for the transmit pathway, and an IQ demodulator for the receive pathway. This IQ modulator and this IQ demodulator are in general impacted by the loss of quadrature between the in-phase pathway (also known by the expression I pathway) and the quadrature pathway (also known by the expression Q pathway). This is illustrated in FIG. 1 and FIG. 2. In FIG. 1 the in-phase pathway is represented by the element feI(t) and the quadrature pathway by the element feQ(t). In FIG. 2 the in-phase pathway is represented by the element frI(t) and the quadrature pathway by the element frQ(t). This quadrature loss is also known by the expression “TX IQ imbalance” and “RX IQ imbalance”. This quadrature loss has significant effects, indeed the least mismatch of phase and/or gain between the I and Q pathways gives rise to a quadrature loss resulting in a self-jamming of the signal transmitted (or received) by itself. This quadrature loss is represented in FIGS. 1 and 2 by the gains gTx and gRx and the phases φTx and φRx, note that if the transmit pathway is not affected by an imbalance then φTx=0 and gTx=1 and if the receive pathway is not affected by an imbalance then pRx=0 and gRx=1. The level of this self-jamming is all the more significant the higher the quadrature loss.
FIGS. 3 and 4 present the effect of this self-jamming between the various signals. In FIG. 3 the elements a), b) and c) correspond respectively to:                the frequency response E′*(−f) of the image signal e′*(t),        the frequency response E′(f) of the signal to be transmitted e(t) and        the frequency response Ŝ(f) of the signal transmitted.The central carrier represents the resultant carrier. The signal transmitted is jammed at one and the same time by its image.        
In FIG. 4 the elements a) and b) correspond respectively to:                the frequency response of the signal at the input of the IQ demodulator, and        the frequency response R′(f) of the signal affected by the IQ imbalance and the continuous component.The central carrier represents the continuous component, and H(f) the frequency response of the channel. In this example, it is noted that the more frequency selective is the channel, the more significant is the impact of the interference of the signal to be received with its image.        
Prior art systems are known which make it possible to compensate for the imperfections of the IQ modulator of the transmit pathway by a pre-compensation, and for the imperfections of the IQ demodulator of the receive pathway by a post-compensation.
FIG. 5 presents a radio post known in the prior art. For example the journal article by B. Razavi, “Design Considerations for Direct-Conversion Receivers,” published in the IEEE journal Transaction on Circuits and Systems II: Analog and Digital Signal Processing, vol. 44, pp. 428-435, in June 1997, presents such a radio post. This system comprises a transmit pathway 501 and a receive pathway 502. These two pathways are connected together, before the transmit/receive antenna. This connection can be effected for example by virtue of a switch 503.
The transmit pathway comprises a first device 504 for frequency transposition of the signal. This first transposition device uses a first transposition frequency. Likewise the receive pathway comprises a second device 505 for frequency transposition of the signal. This second transposition device uses a second transposition frequency.
These two transposition devices cause imperfections known by the expression IQ imbalance and resultant carrier.
Finally the transmit pathway 501 and the transmit pathway 502 comprise respectively a digital-analogue converter 506 and an analogue-digital converter 507. These two converters make it possible to convert respectively a digital sequence into an analogue sequence and an analogue sequence into a digital sequence.
In order to compensate for these imperfections the system of the prior art comprises a pre-compensation device 508 and a post-compensation device 509.
If the parameters used by these pre and post-compensations are known perfectly, the combination pre-compensation followed by an imperfect transmit pathway and the combination imperfect receive pathway followed by a post-compensation behave respectively as an ideal transmit pathway and an ideal receive pathway.
Apparatuses are also known in which the transmit and receive pathways are not connected together. In this case the signals exchanged between the transmit and receive pathways pass through the propagation channel between the transmit and receive antennas. It is possible to apply the invention to a system in which the transmit and receive pathways are situated in distinct housings and are linked only by the radio channel.
Prior art systems are also known which make it possible to determine the imperfections and therefore to determine the pre-compensations or the post-compensations to be applied to the signals. For example patent application WO2008/116821 is known, which presents a scheme for determining the imperfections of a device comprising a transmit pathway and a receive pathway. In this document the imperfections are calculated by carrying out the following steps:                The imperfections of the receive pathway are calculated by supposing the imperfections of the transmit pathway to be negligible. The scheme is therefore biased and approximate on account of this supposition.        The imperfections of the transmit pathway are calculated on the basis of the imperfections of the receive pathway.        The imperfections of the receive pathway are updated on the basis of the imperfections of the transmit pathway. The scheme of this method is therefore iterative.        
The method, described in document WO2008/116821, for determining the imperfections of the transmit pathway and of the receive pathway, is therefore iterative, approximate and biased. Moreover in this method an assumption is made about the frequency response of the looped-back transmit/receive device as a whole. Indeed in this patent application the solution presented operates only if the channel between the transmit and receive pathway does not vary or varies little as a function of the analysis frequency.
The assumption made is that the equivalent channel is considered to be constant or equal for two analysis frequencies.